Electronic transitions electronically nonadiabatic processes

Another topic in the classical treatment of reactive collisions which has advanced considerably in recent years concerns the treatment of electronically nonadiabatic processes. Early work on this topic followed either the semiclassical complex trajectory method of George and Miller,or the more approximate surface hopping model of Tully and Preston.Recent work in this field by McCurdy, Meyer, and Miller " has attempted to develop a purely classical description of the electronic degrees of freedom, thereby replacing the many-surface aspect of the dynamics with extra classical degrees of freedom (one for each surface beyond the first) which represent the collective electronic motions to which the nuclear motions can couple to cause transitions. This means that a multiple-surface problem can now be treated by standard" trajectory methods, which is a considerable computational simplification. Applications to the f ( Pi/2) 2... 

Electron transfer in proteins generally involves redox centers separated by long distances. The electronic interaction between redox sites is relatively weak and the transition state for the ET reaction must be formed many times before there is a successhil conversion from reactants to products the process is electronically nonadiabatic. A Eandau-Zener treatment of the reactant-product transition probability produces the familiar semiclassical expression for the rate of nonadiabatic electron transfer between a donor (D) and acceptor (A) held at fixed distance (equation 1). Biological electron flow over long distances with a relatively small release of free energy is possible because the protein fold creates a suitable balance between AG° and k as well as adequate electronic coupling between distant redox centers. 

The Marcus theory, as described above, is a transition state theory (TST, see Section 14.3) by which the rate of an electron transfer process (in both the adiabatic and nonadiabatic limits) is assumed to be determined by the probability to reach a subset of solvent configurations defined by a certain value of the reaction coordinate. The rate expressions (16.50) for adiabatic, and (16.59) or (16.51) for nonadiabatic electron transfer were obtained by making the TST assumptions that (1) the probability to reach transition state configuration(s) is thermal, and (2) once the reaction coordinate reaches its transition state value, the electron transfer reaction proceeds to completion. Both assumptions rely on the supposition that the overall reaction is slow relative to the thermal relaxation of the nuclear environment. We have seen in Sections 14.4.2 and 14.4.4 that the breakdown of this picture leads to dynamic solvent effects, that in the Markovian limit can be characterized by a friction coefficient y The rate is proportional to y in the low friction, y 0, limit where assumption (1) breaks down, and varies like y when y oo and assumption (2) does. What stands in common to these situations is that in these opposing limits the solvent affects dynamically the reaction rate. Solvent effects in TST appear only through its effect on the free energy surface of the reactant subspace. 

The preceding discussion has been very general, and much of it applies to other types of nonadiabatic process. By far the most important of these is electron transfer (ET). This involves a transition from one diabatic state to another, with each state corresponding to a different charge distribution ... 

Electron tunneling in proteins occurs in reactions where the electronic interaction between redox sites is relatively weak (1-5). Under these circumstances, the transition state for the reaction must be formed many times before there is a successful conversion from reactants to products the process is electronically nonadiabatic. 

M. Gilibert and M. Baer, Exchange processes via electronic nonadiabatic transitions An accurate three-dimensional quantum mechanical study of the F(2P, 2, 2P, 2) + H2 reactive systems, J. Phys. Chem. 98 12822 (1994). 

Energy calculations show that the membrane potential can supply sufficient energy for this transition. The membrane seems to be this structure at which energy transfer takes place through a low energy barrier, and where the uncontroUed diffusion of electrons is prevented by nonadiabatic behavior in the electron transfer process. " The polar electronic structure of lipids and proteins holding vibrating ions is crucial here. 

After these studies we proceed into the world of nonadiabatic theories. We first review briefly in Chap. 4 the very basic and classic theories of nonadiabatic transitions and the ideas behind them. As stressed above, the theories shown in this chapter were developed in the early stage of theoretical chemistry and do not necessarily care about the recent experimental progress in nonadiabatic processes associated with nonadiabatic electron d3mamics in laser fields. But stud3dng these classic theories and the ideas behind is very instructive. 

Nonadiabatic dynamics is a quantum phenomenon which occurs in systems that interact sufficiently strongly with their environments to cause a breakdown of the Born-Oppenheimer approximation. Nonadiabatic transitions play significant roles in many chemical processes such as proton and electron transfer events in solution and biological systems, and in the response of molecules to radiation fields and their subsequent relaxation. Since the bath in which the quantum dynamics of interest occurs often consists of relatively heavy molecules, its evolution can be modeled by classical mechanics to a high degree of accuracy. This observation has led to the development of mixed quantum-classical methods for nonadiabatic processes. 

A further complexity in the simulation of photochemistry and more in general of excited state photoinduced dynamics is that they are intrinsically nonadiabatic processes, in which the coupling between the nuclear and electronic motion leads to nonradialive transitions between electronic states. A generally applicable approach for this purpose is the mixed quantum-classical dynamics in which the nuclear motion is described by classical trajectories obtained in the framework of molecular dynamics on the fly combined with Tully s surface hopping (TSH) procedure... 

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